You will be subject to radiated noise susceptance. However, considering the voltage levels in the primary of an OPT, I doubt it will be noticeable unless you live in a high EMI/RFI environment. You could shield the cable assembly with braid to minimize it.

Safety wise, you are going to be carrying HV through the connecting cable so due diligence is in order. The shield would be a good idea from this prospective as well.

I was also worried about the frequency range of the amplifier, because a shielded cable has a capacitance to ground and a small induction from the cable.
Is there somebody who can simulate this what happens with the bandwith?